We study in this paper the performance of a one-way cooperative transmission system using differential PSK (DPSK) modulation with differential detection. As opposed to previous works which consider either a decode-and-forward (DF) or an amplify-and-forward (AF) relay, we adopt in this paper a phase-forward (PF) relay, whereby each forwarded symbol has constant modulus and a phase equals the phase of the corresponding relay's received symbol. The rationale for adopting this relaying strategy is to avoid potential non-linear amplifier distortion in an amplify-and-forward relay, as well as the implicit information loss/quantization in a DF relay. Through analysis and simulation, we found that this PF-DPSK cooperative transmission scheme has a lower bit-error rate (BER) than that of its DF counterpart. Furthermore, by adopting a threshold-based selective forwarding approach, it can attain a BER similar to that of AF. Finally, we anticipate that PF is most useful in two or multi-way relaying, in which any non-linear amplifier distortion on an AF signal will manifest into significant inter-modulation.